Complex analysis is a branch of mathematics that deals with complex numbers and functions on the complex plane. It incorporates the study of complex functions, complex differentiation, integration in the complex plane, and the theory of residues and singularities. Complex analysis has applications in various fields such as physics, engineering, and computer science. It is also used to study analytic functions, harmonic functions, and conformal mappings. The main objectives of complex analysis include understanding the behavior of functions that are defined on the complex plane and exploiting the deep connections between complex analysis and other areas of mathematics.